2001 - JAMB Mathematics Past Questions and Answers - page 4
31
If y = x sinx, find dy/dx when x = π/2.
A
-π/2
B
-1
C
1
D
π/2
correct option: c
y = x sin x
dy/dx = 1 x sinx + x cosx
= sinx + x cosx
At x = π/2, = sin (π/2) + (π/2) cos (π/2)
= 1 + (π/2) x (0) = 1
Users' Answers & Commentsdy/dx = 1 x sinx + x cosx
= sinx + x cosx
At x = π/2, = sin (π/2) + (π/2) cos (π/2)
= 1 + (π/2) x (0) = 1
32
Find the dimensions of a rectangle of greatest area which has a fixed perimeter p.
A
square of sides p
B
square of sides 2p
C
square of sides (p/2)
D
square of sides (p/4)
correct option: d
Let the rectangle be a square of sides p/4.
So that perimeter of square = 4p
4 x (p/4) = p.
Users' Answers & CommentsSo that perimeter of square = 4p
4 x (p/4) = p.
33
Given the scores: 4, 7, 8, 11, 13, 8 with corresponding frequencies: 3, 5, 2, 7, 2, 1 respectively. Find the square of the mode.
A
49
B
121
C
25
D
64
correct option: b
Mode = score with highest frequency = 11.
Square of 11 = 121
Users' Answers & CommentsSquare of 11 = 121
34
Given the scores: 4, 7, 8, 11, 13, 8 with corresponding frequencies: 3, 5, 2, 7, 2, 1 respectively. Find the square of the mode.
A
49
B
121
C
25
D
64
correct option: b
Mode = score with highest frequency = 11.
Square of 11 = 121
Users' Answers & CommentsSquare of 11 = 121
35
Given the scores: 4, 7, 8, 11, 13, 8 with corresponding frequencies: 3, 5, 2, 7, 2, 1 respectively. The mean score is
A
7.0
B
8.7
C
9.5
D
11.0
correct option: b
Mean = ∑fx/∑f
Mean = (4x3) + (7x5) + ... + (8x1) all divided by 20
Mean = 174/20 = 8.7
Users' Answers & CommentsMean = (4x3) + (7x5) + ... + (8x1) all divided by 20
Mean = 174/20 = 8.7
36
Teams P and Q are involved in a game of football. What is the probability that the game ends in a draw?
A
2/3
B
1/2
C
1/3
D
1/4
correct option: d
P (games end in draw)
=> Team P wins and Q wins
P(P wins) = 1/2
P(Q wins) = 1/2
Therefore P (games ends in draw) = 1/2 x 1/2 = 1/4
Users' Answers & Comments=> Team P wins and Q wins
P(P wins) = 1/2
P(Q wins) = 1/2
Therefore P (games ends in draw) = 1/2 x 1/2 = 1/4
37
If 6Pr = 6, find the value of 6Pr+1
A
30
B
33
C
35
D
15
correct option: a
6Pr = 6 Thus r = 1
N.B 6P1 = \(\frac{\text{6!}}{\text{(6 - 1)!}}\)
= \(\frac{\text{6!}}{\text{5!}}\)
= \(\frac{6 \times \text{5!}}{\text{5!}}\) = 6
6Pr + 1 = 6P2 = \(\frac{\text{6!}}{(6 - 2)\text{!}} = \frac{6\text{!}}{\text{4!}}\)
= \(\frac{6 \times 5 \times \text{4!}}{\text{4!}}\)
= 30
Users' Answers & CommentsN.B 6P1 = \(\frac{\text{6!}}{\text{(6 - 1)!}}\)
= \(\frac{\text{6!}}{\text{5!}}\)
= \(\frac{6 \times \text{5!}}{\text{5!}}\) = 6
6Pr + 1 = 6P2 = \(\frac{\text{6!}}{(6 - 2)\text{!}} = \frac{6\text{!}}{\text{4!}}\)
= \(\frac{6 \times 5 \times \text{4!}}{\text{4!}}\)
= 30
38
Given distribution of color beads: blue, black, yellow, white and brown with frequencies 1, 2, 3, 4, and 5 respectively. Find the probability that a bead picked at random will be blue or white.
A
7/15
B
2/5
C
1/3
D
1/15
correct option: c
Total number of beads = 15.
Number of white beads = 4. => P(white) = 4/15.
Number of blue beads = 1. => P(blue) = 1/15.
P(white or blue) = P(white) + P(blue) = 5/15 = 1/3
Users' Answers & CommentsNumber of white beads = 4. => P(white) = 4/15.
Number of blue beads = 1. => P(blue) = 1/15.
P(white or blue) = P(white) + P(blue) = 5/15 = 1/3
39
Find the variance of 2, 6, 8, 6 2, and 6.
A
6
B
5
C
√6
D
√5
correct option: b
\(The \hspace{1mm}mean \hspace{1mm} \bar{x} = \frac{\sum{x}}{n}=\frac{30}{6}=5\Variance\hspace{1mm}=\frac{\sum({x-\bar{x}})^{2}}{n}=\frac{30}{6}=5\)
Users' Answers & Comments40
Find the number of ways of selecting 8 subjects from 12 subjects for an examination.
A
490
B
495
C
496
D
498
correct option: b
Combination is the (n) number of ways of selecting a number of (r) subjects from n.
nCr = n!/r!(n-r)! = 12! 8! x 4! = 495
Users' Answers & CommentsnCr = n!/r!(n-r)! = 12! 8! x 4! = 495